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      SUBROUTINE <a name="CGBTRS.1"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB,
     $                   INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          TRANS
      INTEGER            INFO, KL, KU, LDAB, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX            AB( LDAB, * ), B( LDB, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CGBTRS.20"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a> solves a system of linear equations
</span><span class="comment">*</span><span class="comment">     A * X = B,  A**T * X = B,  or  A**H * X = B
</span><span class="comment">*</span><span class="comment">  with a general band matrix A using the LU factorization computed
</span><span class="comment">*</span><span class="comment">  by <a name="CGBTRF.23"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the form of the system of equations.
</span><span class="comment">*</span><span class="comment">          = 'N':  A * X = B     (No transpose)
</span><span class="comment">*</span><span class="comment">          = 'T':  A**T * X = B  (Transpose)
</span><span class="comment">*</span><span class="comment">          = 'C':  A**H * X = B  (Conjugate transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KL      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of subdiagonals within the band of A.  KL &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KU      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals within the band of A.  KU &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input) COMPLEX array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          Details of the LU factorization of the band matrix A, as
</span><span class="comment">*</span><span class="comment">          computed by <a name="CGBTRF.49"></a><a href="cgbtrf.f.html#CGBTRF.1">CGBTRF</a>.  U is stored as an upper triangular band
</span><span class="comment">*</span><span class="comment">          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
</span><span class="comment">*</span><span class="comment">          the multipliers used during the factorization are stored in
</span><span class="comment">*</span><span class="comment">          rows KL+KU+2 to 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= 2*KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The pivot indices; for 1 &lt;= i &lt;= N, row i of the matrix was
</span><span class="comment">*</span><span class="comment">          interchanged with row IPIV(i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, the solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      COMPLEX            ONE
      PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LNOTI, NOTRAN
      INTEGER            I, J, KD, L, LM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.84"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           CGEMV, CGERU, <a name="CLACGV.87"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>, CSWAP, CTBSV, <a name="XERBLA.87"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      NOTRAN = <a name="LSAME.97"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> )
      IF( .NOT.NOTRAN .AND. .NOT.<a name="LSAME.98"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) .AND. .NOT.
     $    <a name="LSAME.99"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'C'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( KL.LT.0 ) THEN
         INFO = -3
      ELSE IF( KU.LT.0 ) THEN
         INFO = -4
      ELSE IF( NRHS.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDAB.LT.( 2*KL+KU+1 ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.115"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CGBTRS.115"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 .OR. NRHS.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      KD = KU + KL + 1
      LNOTI = KL.GT.0
<span class="comment">*</span><span class="comment">
</span>      IF( NOTRAN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve  A*X = B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve L*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        L is represented as a product of permutations and unit lower
</span><span class="comment">*</span><span class="comment">        triangular matrices L = P(1) * L(1) * ... * P(n-1) * L(n-1),
</span><span class="comment">*</span><span class="comment">        where each transformation L(i) is a rank-one modification of
</span><span class="comment">*</span><span class="comment">        the identity matrix.
</span><span class="comment">*</span><span class="comment">
</span>         IF( LNOTI ) THEN
            DO 10 J = 1, N - 1
               LM = MIN( KL, N-J )
               L = IPIV( J )
               IF( L.NE.J )
     $            CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
               CALL CGERU( LM, NRHS, -ONE, AB( KD+1, J ), 1, B( J, 1 ),
     $                     LDB, B( J+1, 1 ), LDB )
   10       CONTINUE
         END IF
<span class="comment">*</span><span class="comment">
</span>         DO 20 I = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL CTBSV( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, N, KL+KU,
     $                  AB, LDAB, B( 1, I ), 1 )
   20    CONTINUE
<span class="comment">*</span><span class="comment">
</span>      ELSE IF( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'T'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A**T * X = B.
</span><span class="comment">*</span><span class="comment">
</span>         DO 30 I = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**T * X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL CTBSV( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, N, KL+KU, AB,
     $                  LDAB, B( 1, I ), 1 )
   30    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve L**T * X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>         IF( LNOTI ) THEN
            DO 40 J = N - 1, 1, -1
               LM = MIN( KL, N-J )
               CALL CGEMV( <span class="string">'Transpose'</span>, LM, NRHS, -ONE, B( J+1, 1 ),
     $                     LDB, AB( KD+1, J ), 1, ONE, B( J, 1 ), LDB )
               L = IPIV( J )
               IF( L.NE.J )
     $            CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
   40       CONTINUE
         END IF
<span class="comment">*</span><span class="comment">
</span>      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A**H * X = B.
</span><span class="comment">*</span><span class="comment">
</span>         DO 50 I = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U**H * X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL CTBSV( <span class="string">'Upper'</span>, <span class="string">'Conjugate transpose'</span>, <span class="string">'Non-unit'</span>, N,
     $                  KL+KU, AB, LDAB, B( 1, I ), 1 )
   50    CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve L**H * X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>         IF( LNOTI ) THEN
            DO 60 J = N - 1, 1, -1
               LM = MIN( KL, N-J )
               CALL <a name="CLACGV.199"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>( NRHS, B( J, 1 ), LDB )
               CALL CGEMV( <span class="string">'Conjugate transpose'</span>, LM, NRHS, -ONE,
     $                     B( J+1, 1 ), LDB, AB( KD+1, J ), 1, ONE,
     $                     B( J, 1 ), LDB )
               CALL <a name="CLACGV.203"></a><a href="clacgv.f.html#CLACGV.1">CLACGV</a>( NRHS, B( J, 1 ), LDB )
               L = IPIV( J )
               IF( L.NE.J )
     $            CALL CSWAP( NRHS, B( L, 1 ), LDB, B( J, 1 ), LDB )
   60       CONTINUE
         END IF
      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CGBTRS.212"></a><a href="cgbtrs.f.html#CGBTRS.1">CGBTRS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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